The object of this study is to administer recombinant G-CSF (versus placebo) to newborn infants with neutropenia associated with one of the four following diagnoses: early-onset sepsis: maternal hypertension; late-onset (acquired) sepsis; or necrotizing enterocolitis (NEC). And to assess the effect of such treatment on the following four outcome of variables: blood neutrophil concentration, neutrophil production and function, severity of illness, and duration of illness.